Elliptic curve isogeny class with Cremona label 96558cu (LMFDB label 96558.cs)

• Label: 96558cu
• Number of curves: $4$
• Conductor: $96558$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 96558cu have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(7\)	\(1 - T\)
\(11\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 96558cu do not have complex multiplication.

Modular form 96558.2.a.cu

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 96558cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
96558.cs3	96558cu1	\([1, 0, 0, -19544, 613680]\)	\(466025146777/177366672\)	\(314215878814992\)	\([2]\)	\(409600\)	\(1.4811\)	\(\Gamma_0(N)\)-optimal
96558.cs2	96558cu2	\([1, 0, 0, -138124, -19331476]\)	\(164503536215257/4178071044\)	\(7401707716779684\)	\([2, 2]\)	\(819200\)	\(1.8277\)
96558.cs4	96558cu3	\([1, 0, 0, 22806, -61656066]\)	\(740480746823/927484650666\)	\(-1643095635218509626\)	\([2]\)	\(1638400\)	\(2.1742\)
96558.cs1	96558cu4	\([1, 0, 0, -2196334, -1253022550]\)	\(661397832743623417/443352042\)	\(785425186877562\)	\([2]\)	\(1638400\)	\(2.1742\)